It is famously known that Saint Augustine, Church Father from the late IV^th and early V^th century, was a fluent Latin speaker of Northern African descent, with scholarly consensus on Berber origins. He was famously the bishop of Hippo (modern day Annaba Algeria) but born in Thagaste (same general area). He mentions when he discusses his difficulties to learn Greek (IV, 13) that Latin was not his mother tongue : La difficulté d’apprendre cette langue étrangère assaisonnait de fiel la douce saveur des fables grecques. Pas un mot qui me fût connu ; et puis, des menaces terribles de châtiments pour me forcer d’apprendre. J’ignorais de même le latin au berceau

"The difficulty to learn this foreign language embittered the sweet delights of greek tales. Not a word that I knew, and terrible threats of punishments to force me to learn it. I even ignored Latin at first (in the crib)"

Given the relatively high status of his family, it is plausible that he acquired fluency in Latin at a very early age : Power considers that his first language is likely to have been latin (Power, Kim (1999) "Family, Relatives", pp. 353–354 in Augustine Through the Ages: An Encyclopedia. Allan D. Fitzgerald, ed. Grand Rapids: Wm. B. Eerdmans, ISBN 978-0-8028-3843-8). Miles Hollingworth also suggests that his family, having acquired Roman citizenship more than a century earlier than his birth and being of high status probably spoke latin primarily or exclusively at home ((2013). Saint Augustine of Hippo: An Intellectual Biography. Oxford University Press. pp. 51–52.)

I remember that in his Confessions (one of the first autobiographical texts in the history of western literature), where he discusses his childhood, he mentions in passing that not only was Latin the lingua franca of the region but there were still speakers of a lingua punica, possibly a carthaginian dialect, for instance when he mentions the need for clergymen fluent in the local language to further evangelization of Northern Africa. See for example Saint Augustin et la survivance de la langue punique, Courtois, Christian Comptes rendus des séances de l'Académie des Inscriptions et Belles-Lettres Année 1950 94-3 pp. 305-307.

Remember that the region of modern day Morocco, Algeria and Tunisia had been extensively romanized and colonized as early as I^st century BC (before northern Gaul for instance) : there are Roman ruins in the region on a massive scale (the Bardo Antiquities Museum in Tunis has one of the foremost collections of Roman mosaics in the world). Cato (the Younger), whom you may know as a defender of Republican insitutions during the life of J. Caesar, was born and raised in Utica, in northern Tunisia (the ruins of the city can be visited).

In conclusion, in the 450s, there was probably a widespread use of Latin as a primary language in the middle to upper urban classes in Northern Africa and as a lingua franca, while local languages retained some use in different contexts.

In the Northern Mediterranean, we know from Grégoire de Tours (Historia Francorum) that as late as the VIth century there was some survivance of Gaulish, albeit very limited. Modern French has incredibly little words of Gaulish origin (an example is ruche which means hive, there are also several toponyms and names of rivers predating the Romans). The difference is that for 1500 more years there was continued cultural influence of Latin (through Church, legal uses in the Middle Ages, etc.) while in Northern Africa it switched abruptly to Arabic at the moment of Muslim conquest.